The Standard Model (SM) of particle physics has been very successful in explaining a wide range of experimental observations, and the discovery of the Higgs boson at the Large Hadron Collider has put the SM on a firm ground. However, despite its success in explaining most of the experimental data, the SM can not address certain issues such as the non-zero neutrino masses and the existence of dark matter (DM) . This motivates studies beyond the SM, in particular, models that can accommodate neutrino mass and DM. Among the various scenarios that have been proposed in the literature, the models in which the SM is extended by a U(1) gauge group has received some attention. I will talk about a class of gauged U(1) extensions of the SM, where active light neutrino masses are generated by an inverse seesaw mechanism. Instead of considering one particular model, the U(1) charges of all the fermions can be expressed in terms of the U(1) charges of the SM Higgs and the new complex scalar. I will discuss the results of our comprehensive study of the bounds on the model parameters from low energy neutrino data, vacuum stability, perturbative unitarity and DM as well as collider constraints. In addition to the standard WIMP (weakly interacting massive particles) DM candidates whose relic density is generated by freeze-out, I will also discuss the possibility of generating the sterile neutrino DM relic density by the so-called freeze-in mechanism. Google Meet Link: https://meet.google.com/bpr-exta-fpe

Google meet link: https://meet.google.com/icj-dhkq-gna Biological systems, such as cells, grow, proliferate, and respond to stimuli; behaviors that give them their “lifelike” qualities. These macroscopic behaviors emerge out of complex interactions between chemicals inside a cell, the details of which remain poorly understood. Most importantly, microscopic changes, such as expression of proteins, are not averaged out and they directly affect the emergent behaviors. Therefore, a comprehensive understanding of the macroscopic behavior is only possible through a comprehensive understanding of its emergence from myriads of microscopic interactions. In this talk, I shall describe two systems where I have investigated biological and bio-inspired systems using such an approach. In the first half, I shall describe how self-replicating entities emerge in a nonbiological chemical system. I shall describe a paradox that had plagued this field over three decades and how we resolved it and, in the process, discovered a general design principle for self-replicating materials. In the second half, I shall describe my investigations of cell signaling systems, where I have discovered the impact of spatial heterogeneity on emergent kinetic laws of chemical reactions. Finally, I’ll highlight the impact of these discoveries for future studies of biological and bio-inspired systems.

In Computational Social Choice, we are generally presented with problems where we deal with agents with preferences. One of the central questions there is how to aggregate preferences to achieve a collective decision. For example (i) to form a committee from a set of candidates based on voter preferences, (ii) to find an allocation of agents that respects everyone's preferences, etc. (iii) Another paradigm of problem arises due to the strategic behavior of agents. Here, a set of agents or a central body might want to manipulate the outcome. Problems in this domain range from classical stable matching related problems to relatively new tournament manipulation problems. In this thesis we study one or two problems from each of the three categories mentioned above. They generally involve a large number of agents and are NP-hard. We study these problems in the realm of Parameterized Complexity. Meeting Link: https://meet.google.com/wwt-uvqz-sky

The origin of the tiny neutrino mass can be a key point to study the beyond the Standard Model (BSM) physics. The observation of the neutrino oscillation and flavor mixing can nicely be fitted in the simple extensions of the Standard Model (SM). Such scenarios contain different BSM candidates in the form of fermions and scalars. In this talk we will discuss about a variety of such scenarios which can reproduce the neutrino oscillation. We will also consider some of these scenarios where the BSM particles can be tested at the energy frontier through a variety of interesting signatures.

Identification of palindromes, i.e., words that are symmetric under reversal, have applications to string processing, bioinformatics, error correcting codes, etc. A word is a Watson-Crick (WK) palindrome when the complement of its reverse is equal to itself. It was introduced to study palindromes from the perspective of DNA computing. WK mapping is an antimorphic involution. WK-conjugates of a word is a generalisation of conjugates of a word that incorporates the notion of WK-involution. We investigate scattered palindromic subwords in finite words. We study the distribution of palindromes and WK-palindromes among both the set of conjugates and WK-conjugates of a word. Two-dimensional palindromes were introduced in order to characterize 2D Sturmian words in terms of 2D palindromes. Due to their highly symmetric nature, 2D palindromes have applications in data compression, face recognition, pattern recognition, etc. We enumerate 2D palindromic factors in two-dimensional periodic and aperiodic words.